Artists and scientists rarely know how their original ideas come about. They mention intuition, but cannot say how it works. Moreover, many people assume that there will never be a scientific theory of creativity-for how could science possibly explain fundamental novelties? The very notion seems to be a contradiction in terms. Many ideas we call ''creative'' are merely novel combinations of familiar ideas. But, a deeper type of creativity involves the exploration, and transformation, of conceptual spaces in people's minds. These matters can be described by using computational concepts. Recent computer-modeling suggests how novel combinations of ideas might come about. As for the deeper form of originality, most AI-programs focused on creativity are concerned only with exploring conceptual spaces. However, a few attempt also to transform them.